[C++ 基于Eigen库实现CRN前向推理]

第三部分：TransposedConv2d实现 （含dilation）

• 前言：(Eigen库使用记录)
• 第一部分：WavFile.class (实现读取wav/pcm,实现STFT)
• 第二部分：Conv2d实现
• 第三部分：TransposedConv2d实现 (mimo,padding,stride,dilation,kernel,outpadding)
• 第四部分：NonLinearity （Sigmoid，Tanh，ReLU，ELU，Softplus）
• 第五部分：LSTM
• GITHUB仓库

1. LSTM介绍

1.1 pytorch LSTM介绍

Lstm是RNN网络中最有趣的结构之一，不仅仅使得模型可以从长序列中学习，还创建了长短期记忆模块，模块中所记忆的数值在需要时可以得到更改。

• 遗忘门
  遗忘单元可以将输入信息和隐藏信息进行信息整合，并进行信息更替，更替步骤如右图公式，其中与乘上权重矩阵后，加上偏置项后，经过激活函数，此时输出值为位于[0,1]之间,并将上一个时间步的与激活函数输出值相乘，更新为
  

• 输入门
  当有输入进入时，输入门会结合输入信息与隐藏信息进行整合，并对信息进行更替
  过程与 过程类似，中间公式使用了tanh函数，可以将输出缩放到[-1,1]之间，再更新
  

• 输出门
  输出门也会对输出过程进行控制，与输入门不同的是，输出门使用tannh激活函数
  

1.2 LSTM递推公式

pytorch的lstm递推公式如下图所示。
在pytorch中，4个权重矩阵Wii,Wif,Wig,Wio被合并为一个权重矩阵Wih,Whh也类似，方便一步计算。

1.3 python实现手动lstm

可以根据公式简单的写出手动实现的版本
这是一个两层的lstm，w和b都写死了，就是固定两层的参数。hidden为1024.

def test_lstm(input, wih0, bih0, whh0, bhh0, wih1, bih1, whh1, bhh1):# 手动模拟B, T, F = input.shapehidden_size = 1024inp_pointer = inputfor layer in range(2):h_t, c_t = (torch.zeros(B, hidden_size).cuda(), torch.zeros(B, hidden_size).cuda())output = torch.zeros(B, T, hidden_size).cuda()batch, time, freq = output.shapeif layer == 0:cur_w_ih = wih0cur_w_hh = whh0cur_b_ih = bih0cur_b_hh = bhh0else:cur_w_ih = wih1cur_w_hh = whh1cur_b_ih = bih1cur_b_hh = bhh1for t in range(time):x_t = inp_pointer[:, t, :]gates = x_t @ cur_w_ih.T + cur_b_ih + h_t @ cur_w_hh.T + cur_b_hhi_t, f_t, g_t, o_t = (torch.sigmoid(gates[:, :hidden_size]),  # inputtorch.sigmoid(gates[:, hidden_size:hidden_size * 2]),  # forgettorch.tanh(gates[:, hidden_size * 2:hidden_size * 3]),torch.sigmoid(gates[:, hidden_size * 3:]),  # output)c_t = f_t * c_t + i_t * g_th_t = o_t * torch.tanh(c_t)output[:, t, :] = h_tinp_pointer = outputreturn inp_pointer

另外，还实现了一个双向LSTM的版本，用了一个小样本进行测试，同样参数都是写死了。

def test_lstm():input_size = 4hidden_size = 6num_layer = 2bidirectional = Truedirection = 2 if bidirectional else 1input = torch.Tensor([[[[0.896227, 0.713551],[0.605188, 0.0700275],[0.827175, 0.186436]],[[0.872269, 0.032015],[0.259925, 0.517878],[0.224867, 0.943635]]],[[[0.290171, 0.0767354],[0.251816, 0.31538],[0.828251, 0.730255]],[[0.24641, 0.757985],[0.354927, 0.694123],[0.990138, 0.946459]]]]).float().transpose(1, 2).reshape(2, 3, 4)B, T, F = input.shapelstm = nn.LSTM(input_size=input_size, hidden_size=hidden_size, num_layers=num_layer, batch_first=True,bidirectional=bidirectional)state = OrderedDict()state['weight_ih_l0'] = torch.ones([4 * hidden_size, input_size])state['weight_hh_l0'] = torch.ones([4 * hidden_size, hidden_size]) * 2state['bias_ih_l0'] = torch.zeros(4 * hidden_size) + 0.5state['bias_hh_l0'] = torch.zeros(4 * hidden_size) + 1.0state['weight_ih_l1'] = torch.ones([4 * hidden_size, hidden_size * direction]) * 2state['weight_hh_l1'] = torch.ones([4 * hidden_size, hidden_size]) * 3state['bias_ih_l1'] = torch.zeros(4 * hidden_size) + 0.5state['bias_hh_l1'] = torch.zeros(4 * hidden_size) + 1.0state['weight_ih_l0_reverse'] = torch.ones([4 * hidden_size, input_size])state['weight_hh_l0_reverse'] = torch.ones([4 * hidden_size, hidden_size]) * 2state['bias_ih_l0_reverse'] = torch.zeros(4 * hidden_size) + 0.5state['bias_hh_l0_reverse'] = torch.zeros(4 * hidden_size) + 1.0state['weight_ih_l1_reverse'] = torch.ones([4 * hidden_size, hidden_size * direction]) * 2state['weight_hh_l1_reverse'] = torch.ones([4 * hidden_size, hidden_size]) * 3state['bias_ih_l1_reverse'] = torch.zeros(4 * hidden_size) + 0.5state['bias_hh_l1_reverse'] = torch.zeros(4 * hidden_size) + 1.0lstm.load_state_dict(state, strict=False)# 手动模拟inp_pointer = inputfor layer in range(num_layer):h_t, c_t = (torch.zeros(B, hidden_size), torch.zeros(B, hidden_size))h_t_reverse, c_t_reverse = (torch.zeros(B, hidden_size), torch.zeros(B, hidden_size))output = torch.zeros(B, T, hidden_size)output_reverse = torch.zeros(B, T, hidden_size)batch, time, freq = output.shapecur_w_ih = state['weight_ih_l{}'.format(layer)]cur_w_ih_reverse = state['weight_ih_l{}_reverse'.format(layer)]cur_w_hh = state['weight_hh_l{}'.format(layer)]cur_w_hh_reverse = state['weight_hh_l{}_reverse'.format(layer)]cur_b_ih = state['bias_ih_l{}'.format(layer)]cur_b_ih_reverse = state['bias_ih_l{}_reverse'.format(layer)]cur_b_hh = state['bias_hh_l{}'.format(layer)]cur_b_hh_reverse = state['bias_hh_l{}_reverse'.format(layer)]for t in range(time):x_t = inp_pointer[:, t, :]r_t = inp_pointer[:, time - t - 1, :]gates = x_t @ cur_w_ih.T + cur_b_ih + h_t @ cur_w_hh.T + cur_b_hhgates_r = r_t @ cur_w_ih_reverse.T + cur_b_ih_reverse + h_t_reverse @ cur_w_hh_reverse.T + cur_b_hh_reversei_t, f_t, g_t, o_t = (torch.sigmoid(gates[:, :hidden_size]),  # inputtorch.sigmoid(gates[:, hidden_size:hidden_size * 2]),  # forgettorch.tanh(gates[:, hidden_size * 2:hidden_size * 3]),torch.sigmoid(gates[:, hidden_size * 3:]),  # output)i_r, f_r, g_r, o_r = (torch.sigmoid(gates_r[:, :hidden_size]),  # inputtorch.sigmoid(gates_r[:, hidden_size:hidden_size * 2]),  # forgettorch.tanh(gates_r[:, hidden_size * 2:hidden_size * 3]),torch.sigmoid(gates_r[:, hidden_size * 3:]),  # output)c_t = f_t * c_t + i_t * g_tc_t_reverse = f_r * c_t_reverse + i_r * g_rh_t = o_t * torch.tanh(c_t)h_t_reverse = o_r * torch.tanh(c_t_reverse)output[:, t, :] = h_toutput_reverse[:, time - t - 1, :] = h_t_reverseinp_pointer = torch.cat([output, output_reverse], dim=2)print(inp_pointer.view(2, 3, 2, -1).transpose(1, 2))th_out, (h, c) = lstm(input)print(th_out)

2. 基于Eigen实现C++ 的LSTM推理

2.1 Layer_LSTM.h

//
// Created by 65181 on 2022/10/31.
//#ifndef CRN_LAYER_LSTM_H
#define CRN_LAYER_LSTM_H#include "Eigen"
#include "mat.h"
#include "Eigen/CXX11/Tensor"class Layer_LSTM {
public:Layer_LSTM();Layer_LSTM(int64_t inp_size, int64_t hid_size, int64_t num_layer = 2, bool bidirectional = false);void LoadState(MATFile *pmFile, const std::string &state_preffix);void LoadTestState();Eigen::Tensor forward(Eigen::Tensor &input, std::vector> &h_t,std::vector> &c_t);private:int64_t input_size;int64_t hidden_size;int64_t num_layers;int64_t direction;bool bidirectional;std::vector> weight_ih, weight_hh;std::vector> weight_ih_reverse, weight_hh_reverse;std::vector> bias_ih, bias_hh;std::vector> bias_ih_reverse, bias_hh_reverse;Eigen::Tensor _load_mat(MATFile *pmFile, const std::string &state_name);Eigen::Tensor _uni_lstm(Eigen::Tensor &input, std::vector> &h_t,std::vector> &c_t);Eigen::Tensor _bi_lstm(Eigen::Tensor &input, std::vector> &h_t,std::vector> &c_t);void print2(Eigen::Tensor input);void print3(Eigen::Tensor input);
};#endif //CRN_LAYER_LSTM_H

2.2 Layer_LSTM.cpp

//
// Created by 65181 on 2022/10/31.
//#include "iostream"
#include "../include/Layer_LSTM.h"using namespace std;Layer_LSTM::Layer_LSTM() {this->input_size = 64;this->hidden_size = 64;this->num_layers = 2;this->direction = 1;
}Layer_LSTM::Layer_LSTM(int64_t inp_size, int64_t hid_size, int64_t num_layer, bool bidirectional) {this->input_size = inp_size;this->hidden_size = hid_size;this->num_layers = num_layer;this->bidirectional = bidirectional;this->direction = bidirectional ? 2 : 1;
}void Layer_LSTM::LoadState(MATFile *pmFile, const std::string &state_preffix) {for (int layer_idx = 0; layer_idx < this->num_layers; layer_idx++) {std::string weight_ih_name = state_preffix + "_weight_ih_l" + std::to_string(layer_idx);std::string bias_ih_name = state_preffix + "_bias_ih_l" + std::to_string(layer_idx);std::string weight_hh_name = state_preffix + "_weight_hh_l" + std::to_string(layer_idx);std::string bias_hh_name = state_preffix + "_bias_hh_l" + std::to_string(layer_idx);this->weight_ih.push_back(_load_mat(pmFile, weight_ih_name));this->bias_ih.push_back(_load_mat(pmFile, bias_ih_name));this->weight_hh.push_back(_load_mat(pmFile, weight_hh_name));this->bias_hh.push_back(_load_mat(pmFile, bias_hh_name));if (this->bidirectional) {std::string w_ih_reverse = state_preffix + "_weight_ih_l" + std::to_string(layer_idx) + "_reverse";std::string b_ih_reverse = state_preffix + "_bias_ih_l" + std::to_string(layer_idx) + "_reverse";std::string w_hh_reverse = state_preffix + "_weight_hh_l" + std::to_string(layer_idx) + "_reverse";std::string b_hh_reverse = state_preffix + "_bias_hh_l" + std::to_string(layer_idx) + "_reverse";this->weight_ih_reverse.push_back(_load_mat(pmFile, w_ih_reverse));this->bias_ih_reverse.push_back(_load_mat(pmFile, b_ih_reverse));this->weight_hh_reverse.push_back(_load_mat(pmFile, w_hh_reverse));this->bias_hh_reverse.push_back(_load_mat(pmFile, b_hh_reverse));}}
}Eigen::Tensor Layer_LSTM::_load_mat(MATFile *pmFile, const std::string &state_name) {mxArray *pa = matGetVariable(pmFile, state_name.c_str());auto *values = (float_t *) mxGetData(pa);long long dim1 = mxGetM(pa);long long dim2 = mxGetN(pa);Eigen::Tensor matrix(dim1, dim2);int idx = 0;for (int i = 0; i < dim2; i++) {for (int j = 0; j < dim1; j++) {matrix(j, i) = values[idx++];}}return matrix;
}void Layer_LSTM::LoadTestState() {for (int layer = 0; layer < this->num_layers; layer++) {int64_t _ih_DIM = layer == 0 ? this->input_size : this->hidden_size * this->direction;Eigen::Tensor state_w_ih(this->hidden_size * 4, _ih_DIM);Eigen::Tensor state_w_hh(this->hidden_size * 4, this->hidden_size);Eigen::Tensor state_b_ih(1, this->hidden_size * 4);Eigen::Tensor state_b_hh(1, this->hidden_size * 4);state_w_ih.setConstant(2);state_w_hh.setConstant(2);state_b_ih.setConstant(1.0);state_b_hh.setConstant(1.0);this->weight_ih.push_back(state_w_ih);this->weight_hh.push_back(state_w_hh);this->bias_ih.push_back(state_b_ih);this->bias_hh.push_back(state_b_hh);//        Eigen::Tensor state_w_ih_reverse(this->hidden_size * 4, _ih_DIM);
//        Eigen::Tensor state_w_hh_reverse(this->hidden_size * 4, this->hidden_size);
//        Eigen::Tensor state_b_ih_reverse(1, this->hidden_size * 4);
//        Eigen::Tensor state_b_hh_reverse(1, this->hidden_size * 4);
//        state_w_ih_reverse.setConstant(layer + 1);
//        state_w_hh_reverse.setConstant(layer + 2);
//        state_b_ih_reverse.setConstant(0.5);
//        state_b_hh_reverse.setConstant(1.0);
//        this->weight_ih_reverse.push_back(state_w_ih_reverse);
//        this->weight_hh_reverse.push_back(state_w_hh_reverse);
//        this->bias_ih_reverse.push_back(state_b_ih_reverse);
//        this->bias_hh_reverse.push_back(state_b_hh_reverse);}
}Eigen::Tensor Layer_LSTM::forward(Eigen::Tensor &input,std::vector> &h_t,std::vector> &c_t) {Eigen::Tensor output;if (this->bidirectional) {output = this->_bi_lstm(input, h_t, c_t);} else {output = this->_uni_lstm(input, h_t, c_t);}return output;
}Eigen::Tensor Layer_LSTM::_uni_lstm(Eigen::Tensor &input,vector> &h_t,vector> &c_t) {Eigen::Tensor::Dimensions dim_inp = input.dimensions();Eigen::Tensor out_pointer = input;if (h_t.empty() || c_t.empty()) {for (int idx_layer = 0; idx_layer < this->num_layers; idx_layer++) {Eigen::Tensor ht_zeros(dim_inp[0], this->hidden_size);Eigen::Tensor ct_zeros(dim_inp[0], this->hidden_size);ht_zeros.setZero();ct_zeros.setZero();h_t.push_back(ht_zeros);c_t.push_back(ct_zeros);}}for (int idx_layer = 0; idx_layer < this->num_layers; idx_layer++) {Eigen::Tensor::Dimensions dim_cur = out_pointer.dimensions();int64_t N_BATCH = dim_cur[0], N_TIME = dim_cur[1], N_FREQ = dim_cur[2], N_HIDDEN = this->hidden_size;Eigen::Tensor cur_w_ih = this->weight_ih[idx_layer];Eigen::Tensor cur_w_hh = this->weight_hh[idx_layer];Eigen::Tensor cur_b_ih = this->bias_ih[idx_layer].broadcast(Eigen::array{N_BATCH, 1});Eigen::Tensor cur_b_hh = this->bias_hh[idx_layer].broadcast(Eigen::array{N_BATCH, 1});Eigen::Tensor &cur_ht = h_t[idx_layer];Eigen::Tensor &cur_ct = c_t[idx_layer];
//        print2(cur_w_ih);
//        print2(cur_w_hh);
//        print2(cur_b_ih);
//        print2(cur_b_hh);
//        print2(cur_ht);
//        print2(cur_ct);Eigen::Tensor output(N_BATCH, N_TIME, N_HIDDEN);Eigen::Tensor X_t;Eigen::Tensor gates;Eigen::Tensor i_t, f_t, g_t, o_t;Eigen::array, 1> product_dims = {Eigen::IndexPair(1, 1)};Eigen::array gate_patch = Eigen::array{N_BATCH, N_HIDDEN};for (int t = 0; t < N_TIME; t++) {X_t = out_pointer.chip(t, 1);
//            print2(X_t);
//            print2(X_t.contract(cur_w_ih, product_dims) + cur_b_ih);
//            print2(cur_ht.contract(cur_w_hh, product_dims) + cur_b_hh);gates = X_t.contract(cur_w_ih, product_dims) + cur_b_ih + cur_ht.contract(cur_w_hh, product_dims) +cur_b_hh;
//            print2(gates);i_t = gates.slice(Eigen::array{0, N_HIDDEN * 0}, gate_patch).sigmoid();f_t = gates.slice(Eigen::array{0, N_HIDDEN * 1}, gate_patch).sigmoid();g_t = gates.slice(Eigen::array{0, N_HIDDEN * 2}, gate_patch).tanh();o_t = gates.slice(Eigen::array{0, N_HIDDEN * 3}, gate_patch).sigmoid();
//            print2(i_t);
//            print2(f_t);
//            print2(g_t);
//            print2(o_t);cur_ct = f_t * cur_ct + i_t * g_t;cur_ht = o_t * cur_ct.tanh();
//            print2(cur_ct);
//            print2(cur_ht);output.chip(t, 1) = cur_ht;}out_pointer = output;}return out_pointer;
}Eigen::Tensor Layer_LSTM::_bi_lstm(Eigen::Tensor &input,vector> &h_t,vector> &c_t) {Eigen::Tensor::Dimensions dim_inp = input.dimensions();Eigen::Tensor out_pointer = input;if (h_t.empty() || c_t.empty()) {for (int idx_layer = 0; idx_layer < this->num_layers * this->direction; idx_layer++) {Eigen::Tensor ht_zeros(dim_inp[0], this->hidden_size);Eigen::Tensor ct_zeros(dim_inp[0], this->hidden_size);ht_zeros.setZero();ct_zeros.setZero();h_t.push_back(ht_zeros);c_t.push_back(ct_zeros);}}for (int idx_layer = 0; idx_layer < this->num_layers; idx_layer++) {Eigen::Tensor::Dimensions dim_cur = out_pointer.dimensions();int64_t N_BATCH = dim_cur[0], N_TIME = dim_cur[1], N_FREQ = dim_cur[2], N_HIDDEN = this->hidden_size;Eigen::Tensor cur_w_ih = this->weight_ih[idx_layer];Eigen::Tensor cur_w_ih_reverse = this->weight_ih_reverse[idx_layer];Eigen::Tensor cur_w_hh = this->weight_hh[idx_layer];Eigen::Tensor cur_w_hh_reverse = this->weight_hh_reverse[idx_layer];Eigen::Tensor cur_b_ih = this->bias_ih[idx_layer].broadcast(Eigen::array{N_BATCH, 1});Eigen::Tensor cur_b_ih_reverse = this->bias_ih_reverse[idx_layer].broadcast(Eigen::array{N_BATCH, 1});Eigen::Tensor cur_b_hh = this->bias_hh[idx_layer].broadcast(Eigen::array{N_BATCH, 1});Eigen::Tensor cur_b_hh_reverse = this->bias_hh_reverse[idx_layer].broadcast(Eigen::array{N_BATCH, 1});Eigen::Tensor &cur_ht = h_t[idx_layer * 2];Eigen::Tensor &cur_ht_reverse = h_t[idx_layer * 2 + 1];Eigen::Tensor &cur_ct = c_t[idx_layer * 2];Eigen::Tensor &cur_ct_reverse = c_t[idx_layer * 2 + 1];// cout << "cur_w_ih" << endl << cur_w_ih << endl;// cout << "cur_w_hh" << endl << cur_w_hh << endl;// cout << "cur_b_ih" << endl << cur_b_ih << endl;// cout << "cur_b_hh" << endl << cur_b_hh << endl;// cout << "cur_ht" << endl << cur_ht << endl;// cout << "cur_ct" << endl << cur_ct << endl;Eigen::Tensor output(N_BATCH, N_TIME, N_HIDDEN);Eigen::Tensor output_reverse(N_BATCH, N_TIME, N_HIDDEN);Eigen::Tensor X_t;Eigen::Tensor X_t_reverse;Eigen::Tensor gates;Eigen::Tensor gates_reverse;Eigen::Tensor i_t, f_t, g_t, o_t;Eigen::Tensor i_t_reverse, f_t_reverse, g_t_reverse, o_t_reverse;Eigen::Tensor cur_cat;Eigen::array, 1> product_dims = {Eigen::IndexPair(1, 1)};Eigen::array gate_patch = Eigen::array{N_BATCH, N_HIDDEN};for (int t = 0; t < N_TIME; t++) {X_t = out_pointer.chip(t, 1);X_t_reverse = out_pointer.chip(N_TIME - t - 1, 1);// cout << "X_t" << endl << X_t << endl;// cout << "X_t_reverse" << endl << X_t_reverse << endl;gates = X_t.contract(cur_w_ih, product_dims) + cur_b_ih + cur_ht.contract(cur_w_hh, product_dims) +cur_b_hh;gates_reverse = X_t_reverse.contract(cur_w_ih_reverse, product_dims) + cur_b_ih_reverse +cur_ht_reverse.contract(cur_w_hh_reverse, product_dims) +cur_b_hh_reverse;i_t = gates.slice(Eigen::array{0, N_HIDDEN * 0}, gate_patch).sigmoid();f_t = gates.slice(Eigen::array{0, N_HIDDEN * 1}, gate_patch).sigmoid();g_t = gates.slice(Eigen::array{0, N_HIDDEN * 2}, gate_patch).tanh();o_t = gates.slice(Eigen::array{0, N_HIDDEN * 3}, gate_patch).sigmoid();i_t_reverse = gates_reverse.slice(Eigen::array{0, N_HIDDEN * 0}, gate_patch).sigmoid();f_t_reverse = gates_reverse.slice(Eigen::array{0, N_HIDDEN * 1}, gate_patch).sigmoid();g_t_reverse = gates_reverse.slice(Eigen::array{0, N_HIDDEN * 2}, gate_patch).tanh();o_t_reverse = gates_reverse.slice(Eigen::array{0, N_HIDDEN * 3}, gate_patch).sigmoid();cur_ct = f_t * cur_ct + i_t * g_t;cur_ht = o_t * cur_ct.tanh();cur_ct_reverse = f_t_reverse * cur_ct_reverse + i_t_reverse * g_t_reverse;cur_ht_reverse = o_t_reverse * cur_ct_reverse.tanh();output.chip(t, 1) = cur_ht;output_reverse.chip(N_TIME - t - 1, 1) = cur_ht_reverse;}out_pointer = output.concatenate(output_reverse, 2);}return out_pointer;
}void Layer_LSTM::print2(Eigen::Tensor input) {const Eigen::Tensor::Dimensions &dim_inp = input.dimensions();std::cout << "Variable:" << std::endl;// 0 0std::cout << input(0, 0) << " " << input(0, 1) << " " << input(0, 2) << " ";std::cout << input(0, dim_inp[1] - 3) << " " << input(0, dim_inp[1] - 2) << " "<< input(0, dim_inp[1] - 1);std::cout << std::endl;// 0 -1std::cout << input(dim_inp[0] - 1, 0) << " " << input(dim_inp[0] - 1, 1) << " "<< input(dim_inp[0] - 1, 2) << " ";std::cout << input(dim_inp[0] - 1, dim_inp[1] - 3) << " " << input(dim_inp[0] - 1, dim_inp[1] - 2)<< " "<< input(dim_inp[0] - 1, dim_inp[1] - 1);std::cout << std::endl;
}void Layer_LSTM::print3(Eigen::Tensor input) {const Eigen::Tensor::Dimensions &dim_inp = input.dimensions();std::cout << "Variable:" << std::endl;// 0 0std::cout << input(0, 0, 0) << " " << input(0, 0, 1) << " " << input(0, 0, 2) << " ";std::cout << input(0, 0, dim_inp[2] - 3) << " " << input(0, 0, dim_inp[2] - 2) << " "<< input(0, 0, dim_inp[2] - 1);std::cout << std::endl;// 0 -1std::cout << input(0, dim_inp[1] - 1, 0) << " " << input(0, dim_inp[1] - 1, 1) << " "<< input(0, dim_inp[1] - 1, 2) << " ";std::cout << input(0, dim_inp[1] - 1, dim_inp[2] - 3) << " " << input(0, dim_inp[1] - 1, dim_inp[2] - 2)<< " "<< input(0, dim_inp[1] - 1, dim_inp[2] - 1);std::cout << std::endl;
}

3.参考链接

[1] 实现LSTM-pytorch版